The present invention relates to profiling control systems which use multiple-degree-of-freedom working machines such as robots, machine tools and the like which have at least two degrees of freedom and, more particularly, to a profiling control system for controlling, by means of position and force, a multiple degree-of-freedom working machine such as a robot, a machine tool or the like which performs a profiling operation such as deburring, curved-surface polishing, a measurement of configuration of a curved surface or the like, thereby profiling a given curved surface.
Almost all of the present industrial robots and automatic machines tool operate by means of control of positions on the basis of position information. It is necessary to control the extent of force applied in performing such as operation fitting operations or polishing operations. In order to control the extent of force, it is required to well control both the position and the force. To this end, various studies and research have been conducted. As typical examples, there are a hybrid control in which a position control and a force control are controlled in switched intervals of each coordinate axis, and a compliance control in which a position and a force are related by means of a spring.
Further, in recent years, there is a so-called virtual compliance control as disclosed in "Transactions of the Society of Instrument and Control Engineers (Keisoku Jido Seigyo Gakkai Ronbun-shu)", vol. 22, No. 3 (1986), pp. 343.about.350, JP-A-60-3010 and JP-A-61-7905. The virtual compliance control is one in which a dynamic system having spring.mass.damper is realized virtually. That is, the virtual compliance control is one in which values of m, c and k of the following equation in the dynamic system are given optionally, and their movement is simulated by software, to perform control so as to realize the movement: EQU mx+cx+k.DELTA.x=f.
In order to effect the control in a multiple degree-of-freedom system, the values of m, c and k can be changed at intervals of each axis of the coordinate system. If the values of m, c and k are selected properly or adequately, it is possible to change a characteristic at intervals of each axis. Further, if k=0, the feedback of the position is eliminated so that a force-control mode is realized. If the values of k and c increase so that the force feedback is eliminated, a positioncontrol mode is realized. Thus, it is possible to effect a so-called hybrid control. In this manner, the virtual compliance control can be said to be a control system which includes the hybrid control and the compliance control.
In case where the conventional virtual compliance control is applied to a profiling control system which utilizes the multiple degree-of-freedom working machine, however, profiling of a given curved surface has its limit, and there is such a problem that it is impossible to conduct an adequate and efficient operation.
For instance, as one of operations which is performed by the robot by control of position and force, there is a curved-surface profiling operation in which a work surface is profiled to effect surface polishing, deburring or the like. In this case, a working tool of the robot is controlled so as to move in profile of the work surface. The force and moment applied to the working tool are detected by a force sensor. A case will be considered where the curved-surface profiling operation is effected in application of the virtual compliance control. Here, a moving direction of the working tool is an x-axis direction, and an axial direction of the working tool is a z-axis direction. Description will be made in an x-z plane, for convenience. For example, the values of k and c increase to be hardened, in the x-axis direction, and the working tool is fed at a velocity v.sub.x by the position control. In the z-axis direction, k=0, to release restriction of the position. The working tool is urged with a target force f.sub.r by the force control. At this time, if the force detected by the force sensor is f, the working tool moves in imitation of the following equation, in the z-axis direction: EQU mv.sub.z +cv.sub.z =f-f.sub.r.
Accordingly, under a steady state in which there is no change in velocity, cv.sub.z =f-f.sub.r. Thus, in order to generate the velocity v.sub.z at which the curved surface is profiled, it can be understood that there must correspondingly be a force error .DELTA.f=f-f.sub.r. Here, if the feed velocity v.sub.x in the x-direction is constant, the velocity v.sub.z is in proportion to a gradient of the curved-surface. Accordingly, the force error .DELTA.f is brought to a value which is in proportion to the gradient of the curved surface, so that the urging force -f changes in accordance with the change in the gradient of the curved surface. Now, if the force error permitted or allowed in the profiling operation is .DELTA.f.sub.o, the gradient is as follows which can be followed under the steady state: ##EQU1##
Here, if 1/c increases, the gradient also increases, which can be followed. Since, however, 1/c is brought to a gain (v=1/c.f) of the velocity with respect to the force, increase in 1/c will cause hunting. For this reason, 1/c must decrease, and it cannot because of an increase in the feed velocity v.sub.x with respect to the large gradient. Thus, increasing 1/c is not efficient and lacks practicality.
In this manner, the conventional profiling control system has a limit in profiling a given curved surface.
It is an object of the invention to provide a profiling control system utilizing a multiple degree-of-freedom working machine, in which it is possible to feed the multiple degree-of-freedom working machine at a requisite feed velocity regardless of a gradient of a curved surface, and it is possible to effect adequate and efficient operation.